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A257024
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Number of squares in the quarter-sum representation of n.
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5
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1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 2, 3, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 2, 2
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OFFSET
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0,6
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COMMENTS
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Every positive integer is a sum of at most four distinct quarter squares; see A257019.
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LINKS
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EXAMPLE
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Quarter-square representations:
r(5) = 4 + 1, so a(5) = 2;
r(11) = 9 + 2, so a(11) = 1;
r(35) = 30 + 4 + 1, so a(35) = 2.
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MATHEMATICA
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z = 100; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];
s[n_] := Table[b[n], {k, b[n + 1] - b[n]}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; Take[g, 100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]
sq = Table[n^2, {n, 0, 1000}]; t = Table[r[n], {n, 0, z}]
u = Table[Length[Intersection[r[n], sq]], {n, 0, 250}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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